We will call the object \(R\)  action representer of \(A\)  and denote by \(\mathbb {AR}(A)\) . It is obvious that if such an object exists for a given \(A\) , then it is unique object up to isomorphism with this property. The notion of \(\mathbb {AR}(A)\)  is the same as the notion of actor of the object \(A\) , denoted by \(\operatorname{Actor}(A)\) , in the case of category of interest [1]}, [2]} and it is equivalent to the special case of the notion of split extension classifier for the object defined in semi-abelian categories in pure categorical way [3]}.
